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Principles and Applications of Quantum Chemistry - 1st Edition - ISBN: 9780128034781, 9780128035016

Principles and Applications of Quantum Chemistry

1st Edition

Author: V.P. Gupta
Paperback ISBN: 9780128034781
eBook ISBN: 9780128035016
Imprint: Academic Press
Published Date: 22nd October 2015
Page Count: 478
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Principles and Applications of Quantum Chemistry offers clear and simple coverage based on the author’s extensive teaching at advanced universities around the globe. Where needed, derivations are detailed in an easy-to-follow manner so that you will understand the physical and mathematical aspects of quantum chemistry and molecular electronic structure. Building on this foundation, this book then explores applications, using illustrative examples to demonstrate the use of quantum chemical tools in research problems. Each chapter also uses innovative problems and bibliographic references to guide you, and throughout the book chapters cover important advances in the field including: Density functional theory (DFT) and time-dependent DFT (TD-DFT), characterization of chemical reactions, prediction of molecular geometry, molecular electrostatic potential, and quantum theory of atoms in molecules.

Key Features

  • Simplified mathematical content and derivations for reader understanding
  • Useful overview of advances in the field such as Density Functional Theory (DFT) and Time-Dependent DFT (TD-DFT)
  • Accessible level for students and researchers interested in the use of quantum chemistry tools


High-level students and researchers in chemistry, material science, biochemistry, chemical engineering

Table of Contents


List of Figures

List of Tables




1. Basic Principles of Quantum Chemistry

  • 1.1. Introduction
  • 1.2. Particle–Wave Duality
  • 1.3. Matrix Mechanics and Wave Mechanics
  • 1.4. Relativistic Quantum Mechanics
  • 1.5. Schrödinger Wave Equation
  • 1.6. Operators—General Properties, Eigenvalues, and Expectation Values
  • 1.7. Postulates of Quantum Mechanics
  • 1.8. Hydrogen Atom
  • 1.9. Atomic Orbitals
  • 1.10. Electron Spin
  • 1.11. Linear Vector Space and Matrix Representation
  • 1.12. Atomic Units
  • 1.13. Approximate Methods of Solution of Schrödinger Equation
  • 1.14. Molecular Symmetry

2. Many-Electron Atoms and Self-consistent Fields

  • 2.1. Wavefunction of Many-Electron Atoms
  • 2.2. Slater Determinants for Wavefunctions
  • 2.3. Central Field Approximation
  • 2.4. Self-consistent Field (SCF) Approximation—Hartree Theory
  • 2.5. Electronic Configuration and Electronic States
  • 2.6. Restricted and Unrestricted Wavefunctions

3. Self-consistent Field Molecular Orbital Theory

  • 3.1. Introduction
  • 3.2. Born–Oppenheimer Approximation
  • 3.3. Chemical Bonding and Structure of Molecules
  • 3.4. Molecular Orbitals as Linear Contribution of Atomic Orbitals (LCAO)
  • 3.5. VB Theory for Hydrogen Molecule—Heitler–London Model
  • 3.6. One-Electron Density Function and Charge Distribution in Hydrogen Molecule
  • 3.7. Formation of Molecular Quantum Numbers for Diatomic Molecules
  • 3.8. HF Theory of Molecules
  • 3.9. Closed-Shell and Open-Shell Molecules
  • 3.10. Atomic Orbitals—Their Types and Properties
  • 3.11. Classification of Basis Sets
  • 3.12. Quality of HF Results
  • 3.13. Beyond HF Theory

4. Approximate Molecular Orbital Theories

  • 4.1. Introduction
  • 4.2. Semiempirical Methods
  • 4.3. Semiempirical Methods for Planar-Conjugated Systems
  • 4.4. Comparative Study of the Performance of Semiempirical Methods

5. Density Functional Theory (DFT) and Time Dependent DFT (TDDFT)

  • 5.1. Introduction
  • 5.2. Theoretical Motivation—Thomas–Fermi Model
  • 5.3. Formalism of the DFT
  • 5.4. Kohn–Sham Equations
  • 5.5. LCAO Ansatz in the KS Equations
  • 5.6. Comparison between HF and DFT
  • 5.7. Exchange–Correlation Functional
  • 5.8. Applications and Performance of DFT
  • 5.9. Challenges for DFT
  • 5.10. Time-Dependent DFT
  • 5.11. Approximate Exchange–Correlation Functionals for TDDFT
  • 5.12. Advantages of TDDFT

6. Electron Density Analysis and Electrostatic Potential

  • 6.1. Electron Density Distribution
  • 6.2. Population Analysis
  • 6.3. Electrostatic Potential
  • 6.4. Analysis of Bonding and Interactions in Molecules
  • 6.5. Electrostatic Potential-Derived Charges

7. Molecular Geometry Predictions

  • 7.1. Introduction
  • 7.2. Potential Energy Surface
  • 7.3. Conical Intersections and Avoided Crossings
  • 7.4. Evaluation of Energy Gradients
  • 7.5. Optimization Methods and Algorithms
  • 7.6. Practical Aspects of Optimization
  • 7.7. Illustrative Examples

8. Vibrational Frequencies and Intensities

  • 8.1. Introduction
  • 8.2. Quantum Mechanical Model for Diatomic Vibrator–Rotator
  • 8.3. Vibrations of Polyatomic Molecules
  • 8.4. Quantum Chemical Determination of Force Field
  • 8.5. Scaling Procedures
  • 8.6. Vibrational Analysis and Thermodynamic Parameters
  • 8.7. Anharmonic Polyatomic Oscillator—Anharmonicity and Vibrational Parameter
  • 8.8. Illustration—Anharmonic Vibrational Analysis of Ketene

9. Interaction of Radiation and Matter and Electronic Spectra

  • 9.1. Introduction
  • 9.2. Time-Dependent Perturbation Theory
  • 9.3. Interaction of Radiation with Matter—Semiclassical Theory
  • 9.4. Lasers
  • 9.5. Magnetic Dipole and Electrical Quadrupole Transitions
  • 9.6. Selection Rules
  • 9.7. Electronic Spectra and Vibronic Transitions in Molecules
  • 9.8. Franck–Condon Principle and Intensity Distribution in Electronic Bands
  • 9.9. Oscillator Strength and Intensity of Absorption Bands
  • 9.10. Electronic Spectra of Polyatomic Molecules
  • 9.11. Electronic Transitions and Absorption Bands
  • 9.12. Theoretical Studies on Valence States
  • 9.13. Rydberg States
  • 9.14. Studies of Core Electrons

10. Energy and Force Concepts in Chemical Bonding

  • 10.1. Introduction
  • 10.2. Virial Theorem
  • 10.3. Hellmann–Feynman Theorem
  • 10.4. Hellmann-Feynman Electrostatic Theorem
  • 10.5. Forces in a Diatomic Molecule and Physical Picture of Chemical Bond
  • 10.6. Charge Density Maps

11. Topological Analysis of Electron Density—Quantum Theory of Atoms in Molecules

  • 11.1. Introduction
  • 11.2. Topological Analysis of Electron Density
  • 11.3. Hessian Matrix and Laplacian of Density
  • 11.4. Critical Points
  • 11.5. Molecular Structure and Chemical Bond
  • 11.6. Energy of Atom in Molecule
  • 11.7. Applications

12. Characterization of Chemical Reactions

  • 12.1. Introduction
  • 12.2. Types of Chemical Reaction Mechanisms
  • 12.3. Thermodynamic Requirements for Reactions
  • 12.4. Kinetic Requirements for Reaction
  • 12.5. Potential Energy Surfaces and Related Concept
  • 12.6. Stationary Points and Their Characteristics
  • 12.7. Determination of Potential Energy Surfaces
  • 12.8. Potential Energy Surfaces in Molecular Mechanics
  • 12.9. Prediction of Activation Barrier
  • 12.10. Heats and Free Energies of Formation and Reaction
  • 12.11. Reaction Pathways and Intrinsic Reaction Coordinates
  • 12.12. Photodissociation of Molecules and Bond Dissociation Energies
  • 12.13. Chemical Reactivity and Its Indicators
  • 12.14. Electronegativity and Group Electronegativity
  • 12.15. Chemical Reactivity Indices and Their Mathematical Formulation



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© Academic Press 2016
22nd October 2015
Academic Press
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About the Author

V.P. Gupta

V.P. Gupta

Professor V.P. Gupta, born in December 30, 1942, obtained Ph.D. degree from Moscow, USSR, in 1967. He has been Professor Emeritus and also the Principal Investigator of DST Book-Writing Project under USERS (Utilization of Scientific Expertise of Retired Scientists) scheme at the University of Lucknow, Lucknow. Professor Gupta has 45 years of experience in teaching and research at several universities. He has been Professor and Chairman of the Department of Physics at the University of Jammu, Jammu-Tawi, India, a Visiting Professor of Chemistry at the Université de Provence, Marseilles, France and Professor of Physics at the University of Calabar, Nigeria. He has the distinction of being Professor Emeritus, University Grants Commission (UGC), India, and Emeritus scientist of the Council of Scientific & Industrial Research (CSIR), India, and the All India Council of Technical Education (AICTE), New Delhi, India. He was a visiting scientist/fellow at the University of Helsinki, Helsinki, Finland, and at International Centre for Theoretical Physics, Trieste, Italy; and a member of several national and international academic bodies. Over the past four decades, he has successfully executed several major and minor scientific research projects granted by the national funding agencies such as Department of Science & Technology (DST), Government of India, New Delhi; UGC, New Delhi; CSIR, New Delhi; AICTE, New Delhi; and Indian Space Research Organization (ISRO), Bangalore. His major areas of research are molecular spectroscopy and molecular structure, quantum chemistry, matrix isolation infrared studies, astrochemistry, and laser spectroscopy. He has to his credit 99 research publications and 3 books, including the book published by Elsevier Inc. (Waltham, United States - Academic Press), in October 2015.

Affiliations and Expertise

University of Lucknow, India


"A large number of examples to support different applications have been given. Bibliography at the end of each chapter aims at opening the door for those who intend to pursue quantum chemistry more deeply. Overall, a very useful book for researchers and graduate students." --Zentralblatt MATH

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